Statistical inference for multivariate partially observed stochastic processes with application to neuroscience
Sprache der Bezeichnung:
Englisch
Original Kurzfassung:
In many signal-processing applications, it is of primary interest to decode/reconstruct the unobserved
signal based on some partial observed information. Some examples are automatic speech, face,
gesture and handwriting recognition and neuroscience (ion channels modeling). From a mathematical point
of view, this corresponds to estimate model parameters of an unknown coordinate based on discrete observations
of one or more other coordinates. In this project we consider a partially observed bivariate stochastic
process and discuss it in the framework of stochastic modelling of single neuron dynamics. None of the two
components is directly observed: The available observations corresponds to hitting times of the first components
to the second component and/or measurements at discrete time of the first coordinate. Our aim is
to provide statistical inference of the underlying model parameters, as well as developing suitable numerical
algorithms. This is particularly difficult since the considered process does not fit into the well-known class of
hidden Markov models, requiring the investigation of new ad-hoc mathematical and statistical techniques to
handle it. Our background on mathematical modeling, stochastic numerics, statistical inference for (partially
observed) stochastic processes, hidden Markov models, and mathematical neuroscience, and our expertise
in combining theory and simulations represent a perfect match for the project.
Forschungs-